Answer:
D
Step-by-step explanation:
Answer:
D. 1/3
Step-by-step explanation:
Use the following equation to solve for the slope:
<em>m</em> (slope) = (y₂ - y₁)/(x₂ - x₁).
Let:
(x₁ , y₁) = (0 , 2)
(x₂ , y₂) = (3 , 3)
Plug in the corresponding numbers to the corresponding variables:
<em>m</em> = (3 - 2)/(3 - 0)
<em>m</em> = (1)/(3)
<em>m</em> = 1/3
D. 1/3 is your answer.
~
Answer:
9x² - 33x + 10
Step-by-step explanation:
Given
(3x - 10)(3x - 1)
Each term in the second factor is multiplied by each term in the first factor, that is
3x(3x - 1) - 10(3x - 1) ← distribute both parenthesis
= 9x² - 3x - 30x + 10 ← collect like terms
= 9x² - 33x + 10
Answer: a) 0.0058
b) 0.0026
Step-by-step explanation:
Given : The probability of having clear sunny skies in Seattle in July : p= 0.40
The number of days spent in Seattle in July: n= 18
a) Using, Binomial probability formula : ![P(x)=^nC_xp^x(1-p)^{n-x}](https://tex.z-dn.net/?f=P%28x%29%3D%5EnC_xp%5Ex%281-p%29%5E%7Bn-x%7D)
The probability of having clear sunny skies on at least 13 of those days:-
![P(x\geq13)=P(13)+P(14)+P(15)+P(16)+P(17)+P(18)\\\\=^{18}C_{13}(0.4)^{13}(0.6)^5+^{18}C_{14}(0.4)^{14}(0.6)^4+^{18}C_{15}(0.4)^{15}(0.6)^3+^{18}C_{16}(0.4)^{16}(0.6)^2+^{18}C_{17}(0.4)^{17}(0.6)^1+^{18}C_{18}(0.4)^{18}(0.6)^0](https://tex.z-dn.net/?f=P%28x%5Cgeq13%29%3DP%2813%29%2BP%2814%29%2BP%2815%29%2BP%2816%29%2BP%2817%29%2BP%2818%29%5C%5C%5C%5C%3D%5E%7B18%7DC_%7B13%7D%280.4%29%5E%7B13%7D%280.6%29%5E5%2B%5E%7B18%7DC_%7B14%7D%280.4%29%5E%7B14%7D%280.6%29%5E4%2B%5E%7B18%7DC_%7B15%7D%280.4%29%5E%7B15%7D%280.6%29%5E3%2B%5E%7B18%7DC_%7B16%7D%280.4%29%5E%7B16%7D%280.6%29%5E2%2B%5E%7B18%7DC_%7B17%7D%280.4%29%5E%7B17%7D%280.6%29%5E1%2B%5E%7B18%7DC_%7B18%7D%280.4%29%5E%7B18%7D%280.6%29%5E0)
![=\dfrac{18!}{13!5!}(0.4)^{13}(0.6)^5+\dfrac{18!}{14!4!}(0.4)^{14}(0.6)^4+\dfrac{18!}{15!3!}(0.4)^{15}(0.6)^3+\dfrac{18!}{16!2!}(0.4)^{16}(0.6)^2+(18)(0.4)^{17}(0.6)^1+(1)(0.4)^{18}](https://tex.z-dn.net/?f=%3D%5Cdfrac%7B18%21%7D%7B13%215%21%7D%280.4%29%5E%7B13%7D%280.6%29%5E5%2B%5Cdfrac%7B18%21%7D%7B14%214%21%7D%280.4%29%5E%7B14%7D%280.6%29%5E4%2B%5Cdfrac%7B18%21%7D%7B15%213%21%7D%280.4%29%5E%7B15%7D%280.6%29%5E3%2B%5Cdfrac%7B18%21%7D%7B16%212%21%7D%280.4%29%5E%7B16%7D%280.6%29%5E2%2B%2818%29%280.4%29%5E%7B17%7D%280.6%29%5E1%2B%281%29%280.4%29%5E%7B18%7D)
![=0.00447111249474+0.00106455059399+0.000189253438931+0.0000236566798664+0.00000185542587187+0.000000068719476736](https://tex.z-dn.net/?f=%3D0.00447111249474%2B0.00106455059399%2B0.000189253438931%2B0.0000236566798664%2B0.00000185542587187%2B0.000000068719476736)
![=0.00575049735288\approx0.0058](https://tex.z-dn.net/?f=%3D0.00575049735288%5Capprox0.0058)
b) On converting binomial to normal distribution, we have
![\text{Mean=}\mu=np= 18\times0.40=7.2\\\\\text{Standard deviation}=\sigma=\sqrt{np(1-p)}\\\\=\sqrt{18(0.40)(1-0.40)}=2.07846096908\approx2.08](https://tex.z-dn.net/?f=%5Ctext%7BMean%3D%7D%5Cmu%3Dnp%3D%2018%5Ctimes0.40%3D7.2%5C%5C%5C%5C%5Ctext%7BStandard%20deviation%7D%3D%5Csigma%3D%5Csqrt%7Bnp%281-p%29%7D%5C%5C%5C%5C%3D%5Csqrt%7B18%280.40%29%281-0.40%29%7D%3D2.07846096908%5Capprox2.08)
Let x be the number of days having clear sunny skies in Seattle in July.
Then, using
we have
![z=\dfrac{13-7.2}{2.08}=2.78846153846\approx2.79](https://tex.z-dn.net/?f=z%3D%5Cdfrac%7B13-7.2%7D%7B2.08%7D%3D2.78846153846%5Capprox2.79)
P-value = ![P(x\geq13)=P(z\geq2.79)=1-P(z](https://tex.z-dn.net/?f=P%28x%5Cgeq13%29%3DP%28z%5Cgeq2.79%29%3D1-P%28z%3C2.79%29)
![=1-0.9973645=0.0026355\approx0.0026](https://tex.z-dn.net/?f=%3D1-0.9973645%3D0.0026355%5Capprox0.0026)
Answer:
where is the question
Step-by-step explanation:
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